LU-fuzzy calculus in finance

In this paper we show that the vagueness induced by the fuzzy mathematics (see [5], [7] and [14] for more details) can be relevant in modelling objects in finance (see also [2], [8] and [11]), especially when a flexible parametrization is adopted to represent the fuzzy numbers. Fuzzy calculus for financial applications requires a big amount of computations and the LU-fuzzy representation produces good results due to the fact that it is computationally fast and it reproduces the essential quality of the shape of fuzzy numbers involved in computations. The paper considers the Black and Scholes option pricing formula, as long as many other have done in the last few years (see [3], [13], [15]). We suggest the use of the LU-fuzzy parametric representation for fuzzy numbers, introduced in Guerra and Stefanini (see [10]) and improved in Stefanini, Sorini and Guerra (see [12]), in the framework of the Black and Scholes model for option pricing, everywhere recognized as a benchmark; the details of the computations and an illustrative example are also incuded.